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<span class="kw">let </span><font color="Maroon" title="c1">q1</font>, <font color="Maroon" title="c2">q2</font>, <font color="Maroon" title="c3">p</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">q1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="rltopsp1.html#K1" title="RLTOPSP1:func.1">LSeg</a> <font color="Maroon" title="c2">q2</font>,<font color="Maroon" title="c3">p</font> &amp; <font color="Maroon" title="c1">q1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">q2</font> implies  <a href="topreal6.html#K1" title="TOPREAL6:func.1">dist</a> <font color="Maroon" title="c1">q1</font>,<font color="Maroon" title="c3">p</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="topreal6.html#K1" title="TOPREAL6:func.1">dist</a> <font color="Maroon" title="c2">q2</font>,<font color="Maroon" title="c3">p</font> )</span><br/>





<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:30"/><span class="lab"><font color="Green" title="E23">A1</font></span>: 
<font color="Maroon" title="c1">q1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="rltopsp1.html#K1" title="RLTOPSP1:func.1">LSeg</a> <font color="Maroon" title="c2">q2</font>,<font color="Maroon" title="c3">p</font>
 <span class="kw">and </span><br/><a NAME="E2:30"/><span class="lab"><font color="Green" title="E24">A2</font></span>: 
<font color="Maroon" title="c1">q1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">q2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="topreal6.html#K1" title="TOPREAL6:func.1">dist</a> <font color="Maroon" title="c1">q1</font>,<font color="Maroon" title="c3">p</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="topreal6.html#K1" title="TOPREAL6:func.1">dist</a> <font color="Maroon" title="c2">q2</font>,<font color="Maroon" title="c3">p</font></span><br/>

<a NAME="E3:30"/>
<span class="p1">(<span class="default"><a href="topreal6.html#K1" title="TOPREAL6:func.1">dist</a> <font color="Maroon" title="c2">q2</font>,<font color="Maroon" title="c1">q1</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><a href="topreal6.html#K1" title="TOPREAL6:func.1">dist</a> <font color="Maroon" title="c1">q1</font>,<font color="Maroon" title="c3">p</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="topreal6.html#K1" title="TOPREAL6:func.1">dist</a> <font color="Maroon" title="c2">q2</font>,<font color="Maroon" title="c3">p</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:30"><span class="lab"><font color="Green" title="E23">A1</font></span></a>, <a class="ref" href="jordan1k.html#T29" target="_self" title="JORDAN1K:th.29">Th29</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:30"/>
 <a href="topreal6.html#K1" title="TOPREAL6:func.1">dist</a> <font color="Maroon" title="c1">q1</font>,<font color="Maroon" title="c3">p</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="topreal6.html#K1" title="TOPREAL6:func.1">dist</a> <font color="Maroon" title="c2">q2</font>,<font color="Maroon" title="c3">p</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:30"><span class="lab"><font color="Green" title="E24">A2</font></span></a>, <a class="ref" href="jordan1k.html#T22" target="_self" title="JORDAN1K:th.22">Th22</a>, <a class="ref" href="xreal_1.html#T31" title="XREAL_1:th.31">XREAL_1:31</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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